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This study analyzes the location of vertex and absolute 2-centers of an undirected graph. Under certain assumptions, these locations would be useful for determining the optimal positioning of emergency facilities such as fire stations. Vertex and absolute multi-centers are defined, and a procedure for locating the vertex multi-centers is given. It is shown that certain combinations of arcs and vertices never contain absolute 2-centers, while certain others will always contain a 2-center which is more centrally located than the vertex 2-center. Although no algorithm was found for determining the absolute 2-center of a graph, an algorithm is presented for finding the best 2-centers which exist on arcs incident to the vertex 2-center.

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